Leonid Zhmud The Origin of the History of Science in Classical Antiquity

Introduction to Phaenomena: Eudemus’ History of
Astronomy clearly was not used there.
79
Generally, one has to admit that Tannery’s few arguments in favor of Gemi-
nus are so unconvincing that it seems that only his authority promoted this
idea.
80
Meanwhile, apart from Geminus’ encyclopedia, there were three com-
History 2, 223, favored Eutocius’ version. Mansfeld. Prolegomena, 24 n. 21, opts for
Pappus’ version.
75
Tittel,
op. cit., 1040ff. The same was characteristic of his teacher Posidonius
(fr. 46–47, 195–199 E.-K.). See above, 179 n. 54. Lasserre believed Posidonius to be
the intermediary between Philip and Geminus (
Léodamas, 20 F 17–23, 614f.). On
Geminus, cf. below, 291 f.
76
Tittel,
op. cit., 1048, suggested that Geminus knew Eudemus only through Eratos-
thenes. In this case, Eratosthenes becomes the
Catalogue’s author, which is impos-
sible (see above, 173 n. 28, 174 n. 33).
77
See van Pesch,
op. cit., 112f.
78
This material comes from Posidonius (see above, 179 n. 54) and not from Eudemus.
79
Geminus briefly mentions the Pythagoreans (10.5), Eudoxus’ calendar (108.5. 17)
and parapegma (210.17–18), and in more detail the 19-year cycle of Euctemon,
Philip, and Callippus (120.6ff.) and the 76-year cycle of Callippus (122.16ff.). He-
raclides Ponticus’ name is attested in Geminus’ summary of Posidonius’
Meteo-
rologica (Simpl. In Phys., 291.21f. = Her. Pont. fr. 10 = Posid. fr. 18 E.-K.).
80
The passage that precedes the
Catalogue says that according to Aristotle, sciences
emerged and perished many times (64.9–15). Tannery (
Géométrie, 71, cf. van Pesch,
op. cit., 81) relates this idea to the Stoics rather than to the Peripatetics and, there-
fore, ascribes it to Geminus. Meanwhile, the Aristotelian provenance of this idea is
obvious (
Cael. 270b 19, Pol. 1329b 19), so Proclus rightly refers to Aristotle, and
not to the Stoics. In the passage that follows the
Catalogue, Proclus discusses Eu-
clid’s
Pseudaria, which is now lost. Though Proclus’ praise suggests that this work
was available to him, Tannery excludes this possibility and considers the whole pas-
sage to have been derived from an earlier author. “Who could have been this author,
if not Geminus?” (
Géométrie, 72). Even if Tannery was right in his first supposition
(that Proclus knew
Pseudaria through some intermediary), there is nothing to con-
firm the second one (van Pesch,
op. cit., 81, 83 n.1). Believing his remarks to provide

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Chapter 5: The history of geometry
186
mentaries to the
Elements among Proclus’ sources: by Hero, Porphyry, and
Pappus. There is no point in discussing Hero as a Platonizing redactor of Eude-
mus. Pappus, although he suits this role better than Hero,
81
does not mention
Eudemus in his vast
Collectio and only once in his commentary on book X of
Euclid. Plato’s name occurs only twice in the
Collectio: first, in connection
with the “nature of proportion” and second, concerning the so-called Platonic
bodies.
82
Although Plato is mentioned more often in the commentary on book
X, Pappus was clearly too ‘technical’ an author to be enthusiastic about Plato’s
contribution to geometry.
83
As for the Neoplatonist Porphyry, he is the most ap-
propriate option for the role of the compiler of the
Catalogue. Actually, Tan-
nery had already considered this option, but rejected it in favor of Geminus,
84
who, unlike Porphyry, did not comment on the theorems of Euclid’s book I; his
attention was focused on the foundations of mathematics, including definitions,
axioms, and postulates. Hence Tannery postulates, in a rather mechanical way,
the prevailing influence of Geminus in the first part of Proclus’ commentary,
which comprises the